'Androcracy'/'gynocracy' are hyponyms of, and 'oligocracy'/'oligarchy' is a hypernym of, what term?

What is the term for an oligocratic/oligarchic political system—one in which power is held by a subset of the overall population—where the power allocation is based on one's sex?

A society run by men is an 'androcracy', and one run by women a 'gynocracy'. I am looking for the hypernym of these terms, which would simultaneously be a hyponym of 'oligocracy'. If one does not yet exist, what might we reasonably coin based on whatever the Greek term for 'sex' is, plus -cracy?

(As an extra linguistics question, would 'the mesonym between x and y' be correct to use for what I'm looking for here, rather that 'the hypernym of x and the hyponym of y'?)

1 Answer
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I am unaware that there’s such a word in circulation. Not to worry, though. A feature of English is that you can always use productive prefixes and suffixes (including Greek and Latin ones) to modify an existing word, or, in effect, create a new one by analogy from an existing one, and be clearly understood.

The prefixes andro- and gyno- can be seen as subcategories of geno-, suggesting genocracy. Not quite there yet, since that means “rule by gender” and you’re looking for “rule by a single gender”, but we have mono- for that, so monogenocracy.

Note that you can reasonably argue that all three parts of the word are Greek. For some reason, mixed Latin and Greek roots get some peoples’ hair up.

What context this is useful for, I have no idea.

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